study on the lightship characteristics of …

Brodogradnja/Shipbuilding/Open access Volume 71 Number 3, 2020

37

Chelladurai Sree Krishna Prabu

Nagarajan Vishwanath

Sha Om Prakash

http://dx.doi.org/10.21278/brod71304 ISSN 0007-215X

eISSN 1845-5859

STUDY ON THE LIGHTSHIP CHARACTERISTICS OF MERCHANT

SHIPS

UDC 629.5.012:629.5.013:629.5.012.64:629.5.015.1

Original scientific paper

Summary

Lightship weight and its distribution have significant influence on the intact/ damage

stability and longitudinal strength of the ship. In this study, the range of limiting lightship

longitudinal and vertical centre of gravity for different types of merchant ships have been

determined. The merchant ships considered are bulk carriers, crude oil tankers, liquefied gas

carriers, container ships and pure car carriers. Detailed hull form and general arrangement

layout of the merchant ships were developed. Applicable rules and regulations and design

considerations for each type of merchant ships were considered for this purpose. The principal

dimensions, form coefficients, powering, stability and statutory rules and regulations are

matched to the ships in service. At this stage, different rules and regulations concerning ship’s

stability and trim were considered. Finally, after deducting the vertical and longitudinal center

of gravity of the deadweight components (cargo, fuel and fresh water), the limiting lightship

vertical and longitudinal center of gravity are determined.

Key words: Primary dimensions; lightweight; intact; damage stability; limiting lightship

longitudinal center of gravity; limiting lightship vertical center of gravity

1. Introduction

Ship design is considered more art than science. The design is continually improved

based on the experience gained from similarly built ship types. The knowledge obtained from

existing ships is converted as semi-empirical formula and statistical data. Ship designers

while optimizing ship design consider various aspects like, carrying capacity, propulsion

efficiency, construction cost and freight rate. Besides above safety of crew, cargo and

structural integrity must be satisfied. Last but not the least, the design should have minimum

environmental impact. Some of the design requirements are contradictory. Therefore, rational

choice should be made for owner's requirements. Merchant ships can be divided into two

categories, i.e. deadweight carriers and volume carrier. Deadweight carriers carry relatively

dense cargoes having stowage factor about 1.3 3m t [1]. Typical examples of this ship

category are bulk carriers and tankers. Volumetric carriers carry relatively less dense cargo

having stowage factor more than 2.0 3m t [1]. Typical examples of this ship category are the

http://dx.doi.org/10.21278/brod71304

Sree Krishna Prabu Chelladurai, Study on the lightship characteristic of merchant ships

Vishwanath Nagarajan, Om Prakash Sha

38

passenger ships, containerships, car carriers, LNG and LPG carrier. An important feature of

volumetric carriers is large hold volume. In ship design process, selection of length, beam,

draft, depth, block coefficient, prismatic coefficient and displacement are important elements.

This order is applied to deadweight carriers and logically modified for volumetric carriers [1].

The basic characteristics of different ship’s lightship components, typical sizes and

percentages of weight groups for merchant ships were estimated [2] and updated by

Papanikolaou [1]. In this work [1], the variation of ship characteristics have been presented

with respect to ratios of principal particulars ( /L B , /B T , /L D etc). Statistical analysis of

upper and lower boundaries of hull form coefficients and ratios of main dimensions for

merchant ships were carried out by Strohbusch E. and updated by Papanikolaou [1]. As per

statutory regulations [3], the permissible variation of a ship’s lightship displacement is less

than 2% of the lightship displacement and of the lightship’s longitudinal centre of gravity it is

less than 1% of ship’s length [3]. If the variation is higher, then an inclining experiment needs

to be carried out to determine the new lightship vertical centre of gravity. This shows the

influence of these parameters on the ship’s stability. Sensitivity analysis of the probabilistic

damage stability regulations for Ro-Pax vessel was estimated [4]. Investigation of one large

Ro-Pax ship was carried out, to document the underlying and emerging trends of Ro-Pax ship

design which will help the designer at the early stages. Very few ships have been designed

till date on the basis of probabilistic subdivision regulations. Typical large Ro-Pax vessel was

investigated with variation of parameters, like number, position and optimization of transverse

bulkheads. Also the presence and position of longitudinal bulkheads below the main vehicle

deck, the presence of side casings, and the height of the main deck and double bottom were

considered. Probabilistic damage stability framework was developed to enhance passenger,

ship safety in the maritime industry [5]. The probabilistic framework of the new rules for

damage stability offers flexibility and added degrees of freedom for designers to enhance

safety cost-effectively. Now the trend is towards probabilistic and risk based frameworks to

address ship safety in a scientific manner. Therefore, it is important to understand the

principles and the intention of the ensuing rules and criteria. The problems faced by the

marine industry to cross the bridge from rules-based to risk-based design need to be put into

practice. This paper [5] demonstrates that requirement of scientific and technological

developments are in hand for risk-based design to be fully implemented in the maritime

industry. The optimization of diesel electric machinery system for conceptual ship design

was presented to support selecting the configuration of diesel engines in a machinery system

[6]. The model aims at minimizing investment and operational costs over the ship’s lifetime

when the ship’s operational profiles are assumed to be known. The load distribution on the

engines is considered in the model to ensure that required demand is met with sufficient

power supply for all future operational states. A method for fuel consumption calculation is

presented, based on determining optimal load distribution amongst the engines generalized

specific fuel consumption curve. A parametric method was developed to determine the steel

weight for each main structure to estimate the global design factors with a lower average error

than other methods [7]. This measurement decisively influences the weight calculation and is

also a critical cost item in the tender of a new shipbuilding contract. The principal component

analysis is applied to find the principal influence parameters, including the global and local

design factors, and to calculate the weighting values for each parameter. The obtained weight

distribution to support the various aspects of preliminary design, help to determine the center

of gravity, the design of the ship lines and ship performance evaluation. Cudina and Bezic [8]

evaluated the economics of operating reefer vessels and container ships for carrying same

amount of refrigerated cargo. Detailed general arrangement design of a reefer ship and a

container ship were carried out. Fuel consumption for maintaining the cargo temperature and

for completing similar voyages were compared. It was concluded that the reefer ship's

Study on the lightship characteristic of merchant ships Sree Krishna Prabu Chelladurai,


39

operation is quite economical and further development and improvement of their design was

recommended. Kalajdžic and Momcilovic [9] developed a procedure for determining the

characteristics of an optimum multi purpose cargo vessel in the preliminary design stage.

Statistical analysis of successful multi purpose cargo ships built over the past 30 years was

carried out. Using the proposed set of diagrams and formulas, the ship's principal dimensions

were determined based upon required deadweight as a main prerequisite, as well as optimum

energy efficiency design index, tank capacities, lightweight, etc. It was also concluded that

preliminary design stage is very important, as once the main ship parameters are estimated the

design cannot be repaired later. All the above studies show that improvement in estimation of

ship particulars in preliminary design stage for different ship types still needs improvement.

For some specialized ship types the design charts for preliminary ship design may not be

available in public domain. This paper is a contribution to the preliminary design process for

some popular merchant ship types. In the present study, the approach is as follows. Hull

form and general arrangement design for different types of merchant ships are developed

using commercial design software (MaxsurfⓇ). For this purpose, the rules and regulations for

the applicable ship types are complied with. The lightship weight and its distribution are

determined using existing regression formula and the ship design characteristics. Thereafter

we apply statutory rules and regulations regarding intact and damage stability for the different

ship types. It is well known that maximum permissible KG for ship can be obtained based

on these requirements. Similarly, the forward and aft limit of the ship’s CGL is determined.

The centroid of deadweight components are thereafter determined based on the actual tank

layout and load distribution. Finally, the deadweight component moments are deducted and

the limiting lightship vertical centre of gravity ( LSKG ) and limiting longitudinal centre of

gravity ( LSLCG ) is determined. Based on the analysis, we show the variation of lightship

weight and its centroid for different merchant ship types.

2. Design of ships

The accompanying analysis is based on 58 different hull forms. The hull forms consist

of crude oil tanker, chemical tanker, bulk carrier, container ship, LNG, LPG carrier and pure

car carrier. The numbers of ship and main dimensions are described in Table 1. The principal

dimensions were selected from statistical data of previously built ships. That provides a good

starting point for developing the particulars of hull form and primary dimensions of ships. In

initial design stage, the mission requirements are translated into technical characteristics of

shipbuilding nature.



40

Table 1 Details of different ship types considered for analysis

Sr. no. Ship type Main dimensions

bpL x B x D (m) and year of built

1. Bulk carrier

1 116 18 9.1 2010 5 191.5 33 18.5 2017

2 180 26 14 2008 6 225 33 20.2 2011

3 180 32.3 18 2011 7 233 32.2 19.1 2008

4 184 32.2 17.1 2007 8 301 46.5 24.6 2009

9 221 36.8 19.9 2010

2. Car carrier

1 128 23.4 21 2016 5 188 32.2 33.7 2007

2 165 31.1 30 2008 6 190 32.2 34.7 2010

3 181 25 26 2016 7 194 32.2 32.3 2007

4 185 32 32 2010 8 222.4 32.2 33.7 2008

3. Chemical

tanker

1 114 17.4 9.7 2008 5 177 32.2 18.5 2014

2 135 16.6 6.8 2010 6 187 32 17 2016

3 146 26 13.5 2007 7 219 32.2 20.9 2007

4 158 27 15 2008 8 240 42 21.5 2014

4. Container

carrier

1 128 22.8 14 2007 5 249 32.2 19.5 2007

2 175 27.6 17.1 2006 6 265 40 24 2007

3 185 30 17 2015 7 312.5 42.3 24 2008

4 214 37.5 19.1 2007 8 318 47 26.6 2016

5. Crude

tanker

1 174 32.2 19.1 2007 5 263 46 23 2008

2 175 32 17 2016 6 274 48 22 2007

3 218.5 32.2 20.4 2010 7 320 60 27.1 2010

4 243.5 40.5 22 2016 8 345 60 26 2010

9 236 42 21 2009

6. LNG carrier

1 262 41.5 26.2 2010 5 280 46.5 26.5 2016

2 264 46.8 26 2016 6 280 48.9 27 2016

3 269.5 42 26 2016 7 303 50 27.4 2007

4 277 49 27 2008 8 335 55 30 2008

7. LPG carrier

1 85 15 7.6 2012 5 155 26 16 2010

2 94 17.5 11.7 2006 6 156 25.6 16.4 2016

3 111 19 9.3 2014 7 194.8 32.2 20.8 2012

4 113 19.8 11.2 2007 8 213.5 36.6 22.2 2013

2.1 Design considerations for hull form design

The present work deals with the first two phases (Fig. 1) of ship design, i.e. preliminary

design and concept design. Preliminary design is an elaboration of the various ship-design

steps, partly addressed in the first phase. It involves an accurate determination of ship's

principal characteristics namely, length, beam, depth, draft, block coefficient and effective

powering. It is understood that calculating the above parameters of the ship is subject to



41

compliance with national and international maritime rules. The primary ship dimensions

(length, beam, draft, depth), and hull form characteristics (hull form coefficients, powering,

weight components, stability and trim, freeboard, load line), are required in the first phase of

ship design. After selecting the above basic ship design elements followed by the estimation

of the lightship weight, the displacement of ship is calculated.

Fig. 1 Iterative procedure of estimation of main parameters

The selection of primary dimensions and form coefficients are based on statistical data,

empirical design formulas, coefficient tables and graphs. The above characteristics are guide

to design individual ship type. For all ship types, we should refer the limitations of principal

dimensions (length, beam, draft and depth) based on limitations of ports of call. Besides

above, there are restrictions because of transiting canals, for e.g. Panama Canal, St. Lawrence

Seaway and Suez Canal. The estimation of main dimensions is based on data available from

the similarly built ship, commercial and internal databases. The equivalent data and semi-

empirical formulas are sufficient for the successful application of the empirical method. The

ship's principal dimensions, weight components and powering requirement are dependent on

each other. For displacement ships, for small variation of ship's length, the variation in ship's

resistance and powering may be proportionate [1]. The data of principal dimensions and

coefficients of similar ships help to reduce the design work. It also serves as validation for

computer generated design data. Typical data required for designing different ship types are

shown in Table 2 [1].



42

Table 2 Main particular from similar ship

Sr. no. Type of ship Similar ship main particulars

1. Bulk carriers

Deadweight, speed, main machinery powering, passing

limits through canals

2. Car carrier

Deadweight, number of cars (above and below deck),

speed, powering, and passing limits through canals.

3. Container ships

Deadweight, number of containers (above and below

deck, number of TEU and FEU), speed, powering, and

passing limits through canals.

4. LNG/ LPG carrier

Deadweight, refrigerated cargo hold volume

speed, powering

5. Tankers

Deadweight, speed, powering, passing limits through

canals and narrow straits

In this paper, the sequence of determining the primary dimensions and form

coefficients are briefly described. We first present the principles for the selection of the

primary dimensions and secondly, the different semi-empirical formulas. The procedure for

selecting the main dimensions and form coefficients are based on an iterative approach shown

in Fig. 1. The displacement and speed are primarily dependent on the ship's length. It has a

significant influence on the hull weight, machinery and outfitting. It also reflects on the

construction cost and, it has a strong influence on the ship's resistance and sea keeping

performance. Froude number is representative of the ship's speed. The tanker and bulk

carriers have high BC and

PC coefficients with low Froude number up to 0.20. The above

form corresponds to full hull. They have high frictional resistance as a percentage of total

resistance [2]. For reduction of frictional resistance, ships must have minimum wetted surface

for a given displacement. On the other hand, container and passenger ships have low PC and

BC coefficients with high Froude number above 0.25. They have a significant proportion of

wave/ residuary resistance as a percentage total resistance. To reduce the wave resistance,

relatively slender hulls are designed. For other types of ships the percentage share of the

residuary and frictional resistance components may differ with total resistance [10]. The

position of longitudinal centre of buoyancy varies depending on the longitudinal distribution

of displacement. The basic influencing factors of main dimensions on the steel and outfitting,

and the effect of speed on the lightship weight were investigated by Strohbusch [1].

Strohbusch also investigated the effect of slenderness ratio and prismatic coefficient on ship

hull performance [1]. Ship’s beam has significant influence on stability. An increase of beam

by 10 % leads approximately to a rise in TGM by 30% [11]. Propeller diameter depends on

the draft of the ship. High draft vessels, like tankers and bulk carriers are fitted with a large

diameter propeller for achieving higher efficiency with the low propeller revolution. This is

because higher diameter propeller will have lower revolution. Also, the size of the rudder is

large for better manoeuvrability. Limitation of draft involuntarily increases the primary

dimensions especially the beam of ship. While selecting the draft of the ship, the depth of the

navigation route, water depth of the calling ports, channels, canals, estuaries, bays, and

narrow sea straits must be checked. The selection of the depth is inherently linked to the

permissible draft. Indirectly, it is related to the ship's length (in consideration of the

longitudinal strength) and beam (in consideration of the transverse stability). For example,



43

increase of depth by 10 % causes an increase of the steel weight by 8 % for /L D = 10 or by

4 % for /L D= 14 [2]. One prefers an increase of the ship's depth rather than changes of

other main dimensions in case the ship's hold volume is inadequate. The depth is the

"cheapest" and least problematic primary dimension of a ship. Classification societies define

a limit of the /L D ratio, which varies between 10 to 14 [12]. If / > 14L D , then a special

investigation of longitudinal strength is required. Increase of the depth means reduction of the

ratio /L D . Due to the increase in section modulus, ship’s longitudinal bending stress will

reduce. The increase in depth results in the increase of the hull weight and rise in vertical

center of gravity of the hull [1]. Also, the weight of superstructures and outfitting increases

accordingly. This leads to an increase of the ships KG in all the load conditions. The

loadline rules consider /L D ratio of a standard ship as 15. If the actual /L D ratio is lower,

then the freeboard has to be increased. Here the idea is to have sufficient reserve buoyancy

for ship motions in waves and also during damage stability. The /B T ratio has a strong

influence on the residuary resistance of the ship. It decides the contribution of wave making

resistance to the total resistance of the ship. It is preferred to have the /B T around 2.5 [1].

50 100 150 200 250 300 350

Lbp (m)

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

LC

B /

Lb

p

LCB (+) forward of midship LCB (-) aft of midship

Bulk carrier

Chemical Tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Pure car carrier

70 140 210 280 350

Lbp (m)

0.5

0.6

0.7

0.8

0.9

1

CB

70 140 210 280 350

Lbp (m)

CP

Fig. 2 Variation of different form coefficients with length for different ship types.

The /L B ratio has an influence on the wave resistance of ship. The lower /L B ratio

has an increased effect on wave resistance. The increased beam (reduced /L B ratio)

improves the maneuverability of the ship [1]. As discussed before, container ships and car

carriers have comparatively slim hull. This means PC

and

BC values are low and Fr is

higher as shown in Fig. 2. In container ships, due to low PC , there is concentration of

loaded containers in the midship region below deck. To compensate for this, container ships

are provided with large flare at the forward and aft section for accommodating the containers

on deck. Similarly, in PCCs, huge space is provided above the freeboard deck throughout the



44

length of the ship to accommodate the cars/ trucks. Both the ship types have reduced lower

deck spaces and sharp entrance in the bow region which helps to achieve the relatively high

speed. Figure 2 describes the position of CBL for dead weight and volumetric carriers. The

CBL of the container ships and car carriers are located aft of mid ship, while for the bulk

carrier and tanker vessel it is located forward of mid ship. Load Line Regulations need to be

complied with to achieve the minimum freeboard and bow height for all designs [13]. The

minimum freeboard requirements are classified in two categories. Oil tankers/ gas carriers

come under 'type A' and dry cargo ships come under 'type B' category. The required

freeboard is calculated based on the length of the ship. Thereafter corrections based on the

BC (0.68), depth, sheer of the ship is applied on the tabular freeboard [13]. Figure 3 describes

the minimum freeboard requirement for different length of ship. From Fig. 3 it is

understood, that the volumetric carriers have high freeboard/ depth ratio as compared with the

deadweight carriers. High freeboard ensures that there is sufficient reserve buoyancy and

better survivability in case of hull damage.

70 140 210 280 350

Lbp (m)

0

0.25

0.5

0.75

1

Min

imu

m b

ow

h

eig

ht

/ D

ep

th

0

0.2

0.4

0.6

0.8

Min

imu

mfr

eeb

oard

/ D

ep

th

Bulk carrier

Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Pure car carrier

Required freeboard / Required bow height

Fig. 3 Variation of minimum freeboard and bow height with length for different ship types.

The bow height, is measured at forward perpendicular between summer load line and

the ship’s weather deck or the forecastle deck. Minimum bow height is calculated based on

the regression formula proposed in loadline regulation [13]. All bulk carrier ships are

provided with forecastle as per the loadline regulations [13]. Some of the container ships and

small LPG ships are also provided with forecastle complying with loadline regulations. Some

LPG ships and oil tankers are provided with poop deck meeting the loadline regulations.

Figure 3 shows the freeboard and bow height provided for various ships. The minimum value

required by regulation is also plotted. It is observed that the volumetric carriers have

relatively large freeboard than the dead weight carriers. The freeboard and the bow height for

all types of ships is more than the regulatory requirement. The large bow height helps to

reduce the risk of green-water thereby giving protection against damage of deck cargo or

containers due to large pitching and heaving motions.



45

2.2 Design considerations for general arrangement design

The next stage of ship design is general arrangement. The general arrangement

provides the location/ dimension and extent of engine room, cargo compartment. It also

shows the type and number of bulkheads to be provided on the ship. Using this information

along with the volume and density of cargo in individual compartments, the CGL and KG

position for different loading conditions can be estimated. This information is used to

calculate the stability of ship at a later stage. First, the common regulations applicable for all

the ship types will be described. Forepeak bulkhead is fitted as per classification society's

regulations. Classification society's rules also specify the minimum number of transverse

bulkheads for various ship types. This mainly depends on the type and length of the ship.

Transverse bulkheads need to be located along the length of the ship both from the aspect of

strength and distribution of volume in different cargo holds. This is because for the same

length, we get lower volume in the forward and aft part of the ship due to the narrow ship

sections. All ships are provided with a forward and an aft peak bulkhead. The distance

between the forward collision bulkhead from the forward perpendicular must be within the

limits of 5 % or 10 m and 8 % of bp

L as specified by class rules. From Fig. 4, it is observed

that most of the ships have forepeak tank length nearing the upper limit. This is because the

ships need to achieve minimum draft at forward in the ballast condition for protection against

bottom slamming. The after peak bulkhead is located such that the length of the propeller

shaft is less than the intermediate shaft. This is for the ease of maintenance of propeller shaft.

Steering gear deck is provided as per the parent ship configuration. The aft peak bulkhead

location is also decided based on the required capacity of the aft peak tank. The length of the

engine room compartment depends on ship’s lines plan, the propulsive machinery power and

displacement of ship. In this study, it is based on the similar ship types. When the engine

room is at aft, the aft peak bulkhead coincides with the aft bulkhead of the engine room. The

aft peak bulkhead location is also based on the requirement of minimum volume of ballast

required in aft peak tank for trimming purpose. It is evident from Fig. 4, that the tankers and

liquid gas carrier have larger engine room length. The reason is tankers and liquid gas

carriers have a pump room in the forward part of the engine room. The pump room contains

cargo/ ballast pumps for loading/ unloading the cargo and ballast. The machinery for driving

the cargo/ ballast pumps is located in the forward part of the engine room in these ships. Also

in these ships, engine room is located in aft. Due to narrow section at aft, the engine have to

be located in forward part of the engine room such that sufficient space is available on the

side for maintenance. In case of container ships, the engine room is located near to midship.

As the ship section is wider, smaller length of engine room is sufficient to accommodate the

propulsion machinery with the auxiliaries. In oil tankers and gas carriers, the fuel tanks are

also located within the engine room. While in container ships, the fuel oil tanks are located

away from the engine room.



46

0

0.03

0.06

0.09

0.12

Co

llis

ion

bu

lkh

ea

d

len

gth

/ L

bp

Bulk carrier

Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Pure car carrier

Lower limit

Upper limit

70 140 210 280 350

Lbp (m)

0

0.06

0.12

0.18

0.24

En

gin

e r

oo

mle

ng

th /

Lb

p

Fig. 4 Variation of collision bulkhead length and engine room length with length for different ship types.

The weight estimation at primary stage is an early milestone of ship design. Also, the

accuracy and centroid of different components are vital to calculate the limiting KG . On the

other hand, inaccuracy has a substantial influence on the capacity, speed, and stability of the

ship. Therefore, in the general arrangement design, we must give importance to calculation of

hull, machinery and outfit weight. The ship's displacement can be estimated more accurately

by estimating various weight components that constitute the displacement. This requires

information from similar ships for different designs. There are different methods available for

the estimation of steel weight of ships. The modern ships are usually lighter than older ones

for the same capacity. However, for tankers stringent safety regulations MARPOL and

OPA90 [14] has resulted in double hull construction resulting in increased steel weight. We

assumed that mild steel is used as shipbuilding materials. In recent years, ships are built with

some percentage (30 % to 59 % ) of high tensile steel, to lower lightship weight and increase

the cargo carrying capacity. Different lightship weight components are calculated by using the

semi-empirical formulas proposed by D'Almeida [15]. The lightship weight is considered to

be the sum of three main components:

+ +=LS ST OT MEW W W W (1)

The hull weight, superstructure, machinery weight, and outfit weight are estimated in

the initial stage of design process. Besides above, the lightship weight (LSW ) also includes

lubrication oil, cooling water, feed water (boilers). Steel weight includes the weight of main

hull, bed plates of machinery, etc. Accommodation weight includes the weight of

superstructure and deckhouses. This also includes the weight for the improved quality of

accommodation spaces, sanitary facilities, and air-conditioning besides regulatory

requirements. To comply with regulatory requirements for temperature and noise, larger



47

quantity of insulation materials is used in the engine room and accommodation. Generally, an

increase of ship's length leads to a simultaneous increase of cargo carrying capacity, and steel

weight. From Fig. 5, it is evident that an increase of length leads to linear increment in the

steel weight. Outfit weight includes the weight of all fittings to the "naked" ship and

detachable fitting on hull [16]. Recently, there is an increase in outfit weight due to higher

quality of weather tight hatch covers, cranes and windlass/ mooring winches, deck machinery,

firefighting equipment, etc. From Fig. 5, it appears that an increase of outfit weight is

primarily governed by the ship’s length. From Fig. 5, it is noticed that container ship has the

maximum outfit weight. The reason is container ships have large longitudinal profile area

above the waterline. It is common to accommodate containers on top of the main deck.

Moreover, the containers have to be mandatorily secured by lashing equipment. Typical

weight of lashing equipment is 0.024 t/TEU and 0.031 t/FEU container [1]. The

fundamental component of machinery weight is the main engine, which depends on the speed

and power requirement of different ships [17]. An increase of Froude number indicates an

increased machinery weight and increased values of weight coefficients LS(W /Δ) and

LS / )(W LBD [1]. Besides above, machinery weight is also influenced by the type of ship and

the position of the propulsion machinery (shaft length) and power demand for auxiliary

machineries (pumps, separators, refrigeration etc.) [18].

0

14000

28000

42000

56000

70000

Lig

ht

Sh

ip W

eig

ht

(MT

)

0

600

1200

1800

2400

3000

Ma

ch

ine

ry W

eig

ht

(MT

)

Bulk carrier

Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Pure car carrier

0 1 2 3 4

Displacement * 106 (MT)

0

1400

2800

4200

5600

7000

Ou

tfit

we

igh

t (M

T)

0 1 2 3 4


0

12000

24000

36000

48000

60000

Ste

el

We

igh

t (M

T)

Fig. 5 Variation of different components of lightship weight with displacement for different ship types.

The propulsion machinery can be categorized into three different types like, two stroke

diesel engine, four stroke diesel engine and steam turbine. The four stroke main engine and



48

steam turbine must be coupled with reduction gear or with the accessories of controllable

pitch propeller. If the propulsion machinery is steam turbine, the ship needs the main boiler

to produce steam at high pressure. Some types of ships, container ship (refrigerated

container), LNG and LPG carriers require a high demand for electrical energy for operating

the refrigeration units. Finally, position of the engine room. In container ship it is located

just aft of midship. This implies ship must have a lengthy propeller shaft to connect the

propulsion machinery and the propeller. After identifying all elements which contribute to

the machinery weight, it is evident from Fig. 5 that machinery weights of container ship are

higher when compared with tanker and bulk carrier. Tanker vessels and bulk carriers have

low Froude number that therefore required lower power of the main engine. On the other

hand, container ships have high Froude number ( Fr , 0.25), low PC ,

BC and high

slenderness coefficient. This is because wave resistance is significant proportion to the total

resistance. The container ships require high-speed as it carries perishable cargo in large

volume which must reach the port at scheduled time. Therefore, containerships have

relatively high engine power. It is evident from Fig. 6 that container ship has higher main

engine power, even though their dead weights are low. This leads to an increase of the main

machinery, and auxiliary machinery weight. The auxiliary machineries are supporting the

operation of main machinery (pumps, separators, boiler etc.).

70 140 210 280 350

Lbp (m)

0

14000

28000

42000

56000

70000

Po

we

r (k

W)

Bulk carrier

Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Pure car carrier

Fig. 6 Variation of different main engine power with length for different ship types.

The ballast water capacity is an important element to operate ship safely at sea. The

ballast water capacity is an important feature for both volumetric and dead weight carriers. In

the ballast voyage, ships must satisfy safety requirements like minimum mean draft and

forward draft, maximum permissible trim, and sufficient propeller immersion. Also the ship

shall not trim by bow in loaded departure condition. Therefore, all the ships require a

sufficient amount of ballast to satisfy the above mentioned safety requirements. The capacity

of the ballast tanks shall be determined as described in Table 3 (MARPOL Regulation 18

[14]). The ballast tanks are placed along the ship's sides or wing, double bottom, fore and aft

depending on the type of vessel. In tanker vessel, the whole cargo tank should be protected

by double bottom and side ballast tanks. The side and bottom tank width and height have to

comply with the requirements of MARPOL to avoid the pollution at the time of collision or

grounding [14].



49

Table 3 Criteria for ballast draft condition applied to all ships

Sr. no. Requirements Rules

1. Trim ≤= 0.015*

bpL

MARPOL

2. Mean draft ≥ (2.0 + 0.02 bpL )

3.

Full propeller immersion in sailing

condition

4. Forward draft ≥ 0.04*

bpL

Classification rule

Figure 7 illustrates that volumetric carriers require relatively low ballast water capacity

to achieve the safety requirement as the design draft is less as compared with deadweight

carrier. On the other hand, tankers and bulk carriers have relatively high PC ,

BC and MC

coefficients as shown in Fig. 2 and also, the design draft are relatively high for dead weight

carriers. As a result from Fig. 7, it is obvious that dead weight carriers require higher volume

of ballast water to ensure safety of vessel (MARPOL Regulation 18 [14]). It is evident from

the previous discussions that crude oil tankers and bulk carriers have comparatively

smaller /L B , high /L D ratio with high PC and

BC resulting in high cargo carrying capacity

as seen in Fig. 7.

0 1 2 3 4 Summer


0

80000

160000

240000

320000

400000

Ca

rgo

ca

pa

cit

y (

m3

)

0

3000

6000

9000

12000

15000

Co

nta

ine

r c

ap

ac

ity

(T

EU

)C

ar

ca

rrie

r (n

o. o

f c

ar)

0 1 2 3 4

0

28000

56000

84000

112000

140000

Ba

lla

st

ca

pa

cit

y (

m3

)

Bulk carrier

Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Pure car carrier

Fig. 7 Variation of ballast and cargo capacity with displacement for different ship types.



50

0 1 2 3 4


0

250

500

750

1000

1250

1500

Die

se

l C

ap

ac

ity

(M

T)

0 1 2 3 4


0

2000

4000

6000

8000

10000

12000

HF

O C

ap

ac

ity (

MT

)

0

200

400

600

800

1000

Fre

sh

wa

ter

Cap

ac

ity

(M

T)

Bulk carrier

Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Pure car carrrier

Fig. 8 Variation of HFO, diesel oil and fresh water capacity with displacement for different ship types.

As discussed before, deadweight includes the machinery supplies like heavy fuel oil

(HFO), diesel oil and fresh water. The cooling water for machinery and feed water of boilers

constitute part of lightship weight. HFO is used as fuel in main engine, boilers and auxiliary

engine. A significant quantity of HFO is consumed by the main engine. The consumption of

HFO depends on the main engine power (Fig. 6) and specific fuel consumption. Figure 8

shows that tanker and container ships require large volume of HFO. Also, the HFO carrying

capacity is relatively larger for container ships as compared to other ships, because in every

voyage bunkering cannot be afforded to decrease the turn-around time of the ship. Similarly,

liquefied gas carriers require refrigeration facilities to maintain the temperature (-55 °C ~ -163

℃) in cargo tanks. Therefore, LNG carriers have higher HFO consumption as shown in Fig.

8. In the case of consumption of diesel, the crude oil tanker required relatively large volume

diesel for the inert gas generation unit. Inert gases are pumped into cargo tanks to prevent the

fire hazard. From Fig. 8, one can conclude that tankers require large volume of diesel oil.

MARPOL regulation [19] is followed for double hull protection of fuel oil tanks on all type of

ships. Individual oil fuel tanks capacity is kept less 2,500 m3 for compliance with the

MARPOL regulations [19]. As discussed before, steam is used for different application like

preheating of crude and fuel, and cleaning. From Fig. 8, it is evident that the tankers require

relatively high volume of fresh water as boiler feed water. On the other hand, for LNG

carriers, steam turbines are used as the main propulsion machinery. In LNG carriers, steam is

used in main turbine and auxiliary preheating services. They use the boil off-gases from the

cargo to reduce the fuel consumption of the main boiler. However, they require a significant

quantity of fresh water, to produce steam for running turbines. For all ships, fresh water tanks

capacity and location were based on parent ship arrangements.

Design considerations for oil tanker will be discussed. The present analysis consists of

17 different tanker ship designs. The design for the oil tanker is very elaborate and based on



51

compliance with MARPOL regulations. For oil tankers the following MARPOL regulations

(Annex 1) influence the general arrangement design:

(i) Regulation 18, It specifies the minimum draft and maximum permissible trim during

ballast condition.

(ii) Regulation 19, Double hull and double bottom requirements: It specifies the minimum

width and height of the double side and double bottom in way of the cargo, slop tanks and

pump room. The objective is to avoid pollution at the time of collision or grounding.

(iii) Regulation 23, Accidental oil outflow performance: It is based on probabilistic concept. It

specifies a limit on the amount of oil outflow from the tank in case of damage. The deepest

load line draft is taken as the design draft and the minimum tide is considered as –2.5 m (low

tide). It is assumed that after collision, all cargo in the damaged cargo tanks are spilled out.

Some reduction in oil spillage is given in case of double hull tanks.

(iv) Regulation 28, Subdivision and damage stability: It is based on deterministic concept. It

specifies the damage stability requirements to be complied by the vessel in case of damage. It

is assumed that all the liquid cargo in the damaged cargo tanks are spilled out.

(v) Regulation 29, It specifies the minimum capacity of the slop tanks.

All the ship designs investigated in this paper are assessed to sustain the damage extent

requirement [20] and to fulfill the damage stability requirements as shown in Table 4.

Table 4 Various criteria requirements for intact and damage condition to all type of ships

Sr. no. Ship type

Intact stability

criteria

Damage stability

criteria Damage analysis

1. Bulk carrier IMO MSC.23(59) IMO MSC.216 (82)

Probabilistic

method

2. Car carrier IMO A.749 (18) IMO MSC.216 (82)

Probabilistic

method

3. Container IMO A.749 (18) IMO MSC.216 (82)

Probabilistic

method

4. LNG carrier IGC code IGC code

Deterministic

method

5. LPG carrier IGC code IGC code

Deterministic

method

6. Tankers

MARPOL MARPOL Deterministic

method

Accidental oil

outflow

Accidental oil

outflow Probabilistic

method

The accidental oil outflow in different damage scenario is shown in Fig. 9. The mean

oil outflow is calculated independently for side and bottom damage and then combined into

non-dimensional oil outflow parameter MO as shown in Fig. 9. Figure 9 shows that the

spilled volume varies depending on the side or bottom damage. The estimated oil outflow

from the side damage is higher as compared to bottom damage. The tank’s bottom plate

experience higher hydrostatic pressure as compared to the side tank plates. Therefore, the

bottom oil outflow is lower as compared with the side oil outflow. It is observed from Fig. 9

that the mean outflow gradually reduces with increasing cargo capacity.



52

0 1 2 3 4

Cargo capacity (m3)

0

2500

5000

7500

10000

Sid

e d

am

ag

e (

m3

)

0 1 2 3 4

0

250

500

750

1000

Bo

tto

m d

am

ag

e (

m3

)

Tanker

x 106

0 1 2 3 4

Cargo capacity (m3)

0.01

0.014

0.018

0.022

0.026

Me

an

ou

tflo

w

Actual mean oil outflow

Maximum meanoil outflow

x 106

Fig. 9 Variation of accidental oil outflow with cargo capacity for different tanker ships.

Design considerations for gas carriers will be discussed. For gas carriers general

arrangement design is based on the requirements of International Gas Carrier (IGC) code [21].

The design requirements depend on the type of cargo. The gas carrier ships investigated in

this paper are designed for carrying cargo suitable for “Type 2G/ 2PG” ships. The ships are

mainly intended for carrying LPG, LNG, ammonia and ethane. Even for Type 2G/ 2PG

ships, the design requirements depend on the cargo carrying temperature. If the cargo

temperature is less than -55 ℃, a continuous side longitudinal bulkhead in way of cargo tanks

is provided. If the cargo temperature is between -10 °C and -55 °C, only double bottom is

provided. For all cases, there shall be minimum 0.76 m clearance between the tank and the

ship’s shell plate. The refrigerated cargo tanks must be insulated to maintain the temperature

of the cargo tank and prevent boil-off. The insulated independent tanks are located in hold

space. In case of independent tanks, minimum spacing must be provided between the

insulation and the ship structure to permit passage of personnel for inspection. In case of

membrane tanks, when insulation is applied on one side of the main hull structure, the other

side shall be always accessible for inspection. Therefore, for membrane type LNG ships,

between two cargo tanks, void space/ cofferdam shall be provided. Similarly sufficient size

of opening must be provided on horizontal and vertical structural members for taking out

injured personnel strapped on stretcher from the cargo/ ballast tank spaces. Therefore, the gap

between the cargo tank and the main hull and depth and width of the double bottom and

double side spaces shall be carefully designed [21]. In this paper all LPG carriers have

independent self supporting tanks. For LNG carriers, both independent self supporting tank

and membrane type tank designs are considered. In LNG carriers, there are some differences

between the layout of independent type tank and membrane type tank design. In case of

independent type tank design, a number of large diameter spherical tanks are placed along the

ship's length. The spherical tank diameter depends on ship's beam. Each one of the spherical

tank, is insulated from outside. The hold space supporting the spherical tank is covered by

weathertight steel plate. In membrane type design, void space is provided between transverse

bulkheads on which the membrane type insulation is applied. On the deck, void space is



53

provided above the cargo tank for compliance with regulation. Therefore, length and beam

are an important factor to attain the cargo capacity of LPG/ LNG carrier. For both the LPG

and LNG ships, water ballast tanks, configuration is provided as per parent ship design

configuration. There are some differences in the deterministic damage stability calculations

for oil tankers and gas carriers as described in Table 5. This will influence the

limiting LSKG and LSLCG characteristics of these ship types.

Table 5 Difference between the damage stability requirements of oil tanker and liquid gas carrier

Sr. no. Oil tankers Gas carriers

1

Tankers of more than 225 m in length

should be assumed to sustain damage

anywhere in its length.

A type 2G ship of more than 150 m in

length should be assumed to sustain

damage anywhere in its length.

2

Oil tankers 20,000 tonnes deadweight

and above, shall be able to sustain

bottom raking damage. Not applicable.

3

The angle of heel due to

unsymmetrical flooding shall not

exceed 25°. This angle may be

increased up to 30° if no deck edge

immersion occurs.

The angle of heel due to

unsymmetrical flooding should not

exceed 30°.

Design considerations for bulk carrier will be described. The top side tanks were

designed based on angle of repose. The bottom hopper tanks were designed based on parent

ship configuration. Most of the bulk carriers are single hull construction. The common

design feature of the ship is to achieve maximum volume in cargo holds to accommodate

maximum cargo quantity, up to the maximum allowable draft. Bulk ore carriers are designed

for "alternate hold loading" condition for stability and motion considerations. This means the

cargo can be loaded in "alternate holds" i.e. odd number (1, 3, and 5) of holds. This loading

pattern significantly increases the shear force and bending moment on the ship. It also

requires extra strengthening of the tank top plating in order to endure higher cargo loading.

Their longitudinal strength need to be investigated in detail for this purpose.

For PCC ships ballast capacity is checked for minimum sailing draft requirements. The

freeboard deck is fixed based on the cargo loading / unloading ramp location. The numbers of

transverse bulkheads are kept to a minimum for ease of loading / unloading cargo. Above the

freeboard deck, several decks are provided for storing the cargo. However these deck are non

watertight and do not contribute to either reserve buoyancy or structural strength. For some

container ships, the accommodation is located in the forward side. The cargo holds are also

provided at aft. The cargo hold lengths were based on standard container sizes. Transverse

non watertight bulkheads were provided based on parent ship design. The side tanks

boundaries were made vertical and sizes were compatible with the standard container

dimensions. Container ships during some voyages may carry less number of loaded containers

onboard and significant amount of empty containers may be carried on top two tiers of deck.

This can cause a rise in KG of ship. To make sure that the ship has adequate TGM , ballast

water may be carried in the partially loaded condition. In practice, each ship type may

experience different loading condition. Due to this the vessel may trim based on the CGL

position. In all the loading condition, it is preferred to have trim by aft.



54

3. Method of analysis

In this section, the analysis methodology will be described as shown in Fig. 10. The

analysis is carried out in 2 steps. First, the limiting LSLCG and LSKG is determined using

intact stability rules. Thereafter, further restrictions are imposed on LSLCG and LSKG

based on damage stability requirements.

Start

Intact LCG limit

Intact stability

Damage extent

Damage LCG and KG Limit

Damage stability

End

Loading conditionCargo densityTank levelPermeability

TrimFore & aft draft

GZ curve Initial GMt

Probabilistic Deterministic

MARPOL IGC code IMO Msc 216

Intact KG limit

Fig. 10 Iterative procedure of estimation of lightship LSLCG and LSKG of various ships

First, intact stability analysis will be described. Different intact stability loading

conditions namely, "loaded departure condition", "loaded arrival condition", "ballast

departure condition" and "ballast arrival condition" specified in the regulations are developed

for each ship type [13] and the intact stability criteria requirement shown in Table 6. For oil

tankers and gas carriers in "loaded departure condition", the cargo holds are filled up to 98 %

and fuel oil, diesel oil, fresh water are filled up to 95 % of full capacity. In "loaded arrival

condition" the fuel oil, diesel oil and fresh water are assumed to be consumed 85 % of full

capacity in transit and the cargo quantity remains as 98 % . For LNG carrier 0.2 % boil off is

assumed. In case of bulk carriers, for the “loaded departure condition”, the cargo holds are

loaded for “uniform” and “alternate hold” loading condition respectively.



55

Table 6 Criteria requirements for intact condition to all type of ships

Sr. no. Criteria Value Criteria

1.

O30

0

G dZ ≥3.1513 m.deg IMO intact stability

requirements [3]

IMO intact stability

requirements [3]

2.

O40

0

G dZ ≥ 5.1566 m.deg

3.

O

O

40

30

G dZ ≥ 1.7189 m.deg

4. Minimum GZ ≥ 0.2 m

5. Maximum GZ should occur at ≥ 25˚

6. Initial TGM ≥ 0.15 m

In case of container ships, the average weight of containers (14 tonnes) in the cargo

hold and deck is considered to achieve the desired draft for the “loaded departure condition”.

In case of PCC ship, the loading of cars is carried out in the hold to achieve the desired draft

for the “loaded departure condition”. For all the ships, ballast tanks are suitably filled up to

comply with the regulations for “ballast departure condition”. For bulk carriers, container

ships and PCC ships, loading of fuel oil, fresh water is carried out in the same manner as for

the oil tankers and gas carriers. All the ships were loaded to respective ballast and loaded

draft.

For oil tankers and gas carriers, the additional “in port” operating condition was checked.

During this condition, the cargo tanks are unloaded and the ballast tanks are loaded

simultaneously. There will be a situation where all the cargo and ballast tanks are slack

simultaneously. This will increase the free surface effect. In this condition, it must be

ensured that TGM ≥ 0.15 m.

(1) In "ballast departure condition", the cargo tanks/ holds are empty. The ballast tanks, fuel

oil, diesel oil and fresh water tanks are filled up to 95 % of full capacity. The tank

capacities and arrangement are so designed that the ballast draft satisfies full propeller

immersion, minimum trim by aft, minimum mean draft and minimum draft at forward to

prevent slamming. The conditions are described in Table 3. In ballast arrival condition at

the port the fuel oil, diesel oil, fresh water tank quantity was consumed to 50 % or 15 %

of full capacity. For some ships leftover of 15% of fuel is unlikely due to large HFO

capacity.

(2) The limiting LSKG at any desired draft is determined for complying with the intact

stability condition as shown in Eq. 1 and other rules are described in Table 6. O30

0

G dZ >= 3.1513 m.deg (1a)

( )O30

1

0

sin KN KG d − >= 3.1513 m.deg (1b)



56

1KG ≤

O

O

30

0

30

0

3.1513

sin

KN d

d

−

(1c)

MaxKG ≤ Min ( )1 2 3 4 5, , , ,KG KG KG KG KG (1d)

Here 1KG , 2KG , 3KG , 4KG and 5KG are the limiting KG ’s corresponding to each rule

requirement for a particular loading condition. In Eq. 1d, MaxKG corresponds to each one

of the loaded condition. The LSKG can be calculated for each loading condition as shown in

Eq. 2. The weight and KG of individual components like cargo, ballast, fuel and fresh water

were determined as per the geometry of each hold/ tank.

LSKG

≤

( ) ( )1

* *N

i i

iMax

LS

KG Weight KG

W

=

− (2)

From Eq. 2, LSKG is determined for several ship loading conditions. The minimum LSKG from all the displacement conditions is the global maximum as it will satisfy all the limiting

equations. In this numerical computation process, approximate values of LSKG and LSLCG

are required as input. The LSLCG corresponding to maximum permissible trim by aft is

given as the input. The LSKG calculated as per Schneekluth’s method [2] is given as input.

(3) The limiting CGL at any desired draft is determined for complying with the intact

stability condition as shown in Eq. 3.

0

≤ ( )CB CG

TC

L

M

L − ≤ bp

0.015L

(3)

As per Eq. 3, the vessel is not permitted to trim by forward in any sailing condition. For some

arrival conditions, due to consumption of fuel oil and fresh water, the vessel may trim by

forward. Ballast water is taken on board to make the trim by forward equal to 0 m. From Eq.

3, it can be observed that ship’s CGL have an aft and forward limit. The limiting range of

LSLCG , for each loading condition, can be obtained by logically modifying Eq. 3. The range

of LSLCG which satisfies all the loading condition will be the acceptable range of LSLCG

for the ship type investigated. For the selected range of LSLCG , all intact stability

requirements described in Table 6 will be complied with. In this numerical computation

process, the values of LSKG and LSLCG are required as input. The LSLCG corresponding

to maximum permissible trim by aft is given as the input. The LSKG

calculated as per

Schneekluth’s method [2] is given as input.

The LSKG and LSLCG limits determined earlier are now checked for compliance with

the damage stability requirements. During damage stability calculations it is implicitly



57

assumed that the lightship weight, LSKG and LSLCG do not change after the damage. This

could be unlikely during heavy damage. However, for the purpose of determining limiting

LSLCG and LSKG , this assumption needs to be made. First the computations for

deterministic damage stability will be described. This is applicable for oil tankers, gas

carriers and ships complying with damage stability rules of load line regulations. During

asymmetric damage, the inferior part of the DamagedGZ curve is considered for compliance

with rules. The following damage cases are checked:

(1) The longitudinal, transverse and vertical extent of damage is applied as specified in

MARPOL [14], IGC [21] and Loadline rules [13]. Single/ multiple compartment damage

for cargo area and engine room is applied as per rules.

(2) When a loaded tank is damaged, the liquid inside the tank (cargo or fuel or freshwater) is

assumed to be lost from the damaged tank. In this case the displacement and centre of

gravity of the ship before and after the damage will be different.

(3) When a loaded cargo hold is damaged, its permeability is considered for damage stability

as per rules. For example, in case of bulk carrier, PCCs and container ships, the entire

hold cannot be flooded with water due to the presence of cargo. The permeability values

used for damage stability calculation are described in Table 7 [3].

(4) For double bottom/ double side ships, in the loaded condition, the damage to only outer

hull is also checked. In this case, usually there is no change in the displacement or the

centre of gravity of the ship. This is because double hull spaces are empty during loaded

condition. This includes the “bottom raking damage” for oil tankers. Here, the outer hull

is damaged to a length, as specified in the rules due to grounding. This damage condition

imposes strict requirement on the water ballast tank design configuration. The “bottom

raking damage” is applied only for the oil tankers (MARPOL rule requirement) and not

the gas carriers. Also, the permeability of a tank containing liquids is assumed that the

contents are completely lost from that tank and replaced by water.

Table 7 Permeability of different tanks and compartment of ships

Sr. no. Space Permeability

1 Appropriated to stores 0.60

2 Cargo liquids 0.70

3 Container spaces 0.70

4 Dry cargo space 0.70

5 Ro-Ro spaces 0.90

6 Occupied by accommodation 0.95

7 Occupied by machinery 0.85

8 Void spaces 0.95

9 Consumable liquids 0.95

The damage stability requirements are different for oil tankers, gas carriers and general

cargo ships. In case of oil tankers and gas carriers, the damage stability check is only done

for loaded condition [14], [21]. The damage stability survival requirements are not applied to

the ship in the ballast condition. All the tanker designs are assessed to sustain the damage

requirement [20] to fulfil the damage stability requirements as shown in Table 4. The damage



58

stability requirements for gas carriers were checked as per IGC code as described in Table 8

[21]. The procedure followed is same as that for oil tankers. The intact and damage criteria

requirements are shown in Tables 6 and 8.

Table 8 Various criteria requirements for damage condition to all type of ships

Sr. no. Criteria MARPOL IGC code IMO MSC. 216 (82)

1.

01

1

+20

GZ d

≥ 1.002 m.deg ≥ 1.002 m.deg ----

2.

Minimum damage

GZ

at least 0.1 m

between 1 and

1 +

20°

at least 0.1 m

between 1 and

1 +

20°

at least 0.120 m

3.

Maximum

permissible heel

angle after damage

≥ 25° ≥ 30° ≥ 30°

The limiting LSKG at any desired damaged loading draft is determined for complying

with the damage stability rules as shown in Eqs. 4 and 5.

0.0175 m.rad ≤

O1

1

+20

Damaged GZ d

(4a)

0.0175 m.rad ≤ ( )O

1

1

+20

Damagesin KN KG d

− (4b)

Damage1KG ≤

( )

O1

1

O1

1

+20

+20

Damage 0.0175

sin

KN d

d

−

(4c)

0.1 ≤ ( )DamageMax GZ for 1 ≤ ≤ 0

1+20 (5a)

0.1 ≤ ( ) Damage2DamageKNMax KG− for 1 ≤ ≤ 0

1+20 (5b)

Damage2KG ≤ ( )DamageKN 0.1Max − for 1 ≤ ≤ 0

1+20 (5c)

1 ≤

25 , if deck immersion occurs

30 , if no deck immersion

for oil tankers (5d)

1 ≤ 30 for gas carriers (5e)

( )DamageMax

KG ≤ Min ( )Damage1 Damage2,KG KG (5f)



59

Here Damage1KG and Damage2KG are the limiting DamageKG corresponding to each rule

requirement. In case of damage stability, it may be noted that for each loading condition there

are several possible combination of damages. ( )DamageMax

KG Corresponds to all possible

damages for each loading condition. The limiting LSKG can be calculated for each loading

condition as shown in Eq. 6. The weight and KG of individual components like cargo,

ballast and fuel were determined as per the exact geometry of the compartment. In case of oil

tankers and gas carriers, the contents of the damaged tanks are assumed to be completely lost.

In case of bulk carrier and container ships, permeability of the damaged cargo tank is

considered.

LSKG

≤

( )( ) ( )Damage i

1

DamageMax

LS

* Weight *

W

N

i

i

KG KG=

− (6)

From Eq. 6, LSKG is determined from several damaged ship loading condition. The

minimum LSKG

from the intact and damaged stability conditions is the global maximum as

it will satisfy all the limiting equations. The LSLCG value corresponding to maximum

permissible trim by aft was used during the damage stability calculations for determining the

limiting LSKG . The limiting CGL at any desired draft is determined for complying with the

damage stability condition as shown in Eq. 7.

Damage ForwardTrim

≤ ( )

TC

Damage CB CG Damage

Damage( )

L L

M

−

≤ Damage AftTrim (7)

A ship is assumed to survive a damage condition if the final waterline, taking into account

sinkage, heel and trim, is below the lower edge of any opening through which down flooding

may take place. It is difficult to get a mathematical expression for CGL using the ship

geometric particulars from Eq. 7 as is done for KG from Eqs. 4 and 5. Therefore, an iterative

method is followed in this paper for this purpose. The LSLCG lower and upper limit

determined from the intact stability conditions are used during the damage stability

conditions. The number of damaged combinations for each loaded conditions is very high.

The damage stability calculations are first carried out using the LSLCG lower and upper

limit. If all the damage stability rule requirements are satisfied, then the intact stability

LSLCG lower/ upper limits are retained. If not, the upper/ lower limit, as the case may be, is

decremented by 0.01bp

L % in steps and the damage stability calculations are repeated. The

process is continued till the assumed LSLCG upper/ lower limit meets all the damage

stability requirements. It is ensured that the vessel remains in floating condition (with heel

and trim) as per the requirements of MARPOL/ IGC for all the permissible damage cases.

Therefore, the final limiting values specified would comply with both the intact and damage

stability requirements as described in Fig. 10. The KG

calculated as per Schneekluth’s

method [2] is given as input while computing LSLCG .

The damage stability calculation for general cargo ships will be described. The ships

under this category are bulk carrier, container ship and pure car carrier. For general cargo

ships, damage stability is checked as described in Table 8. The probabilistic methodology is

used for this purpose. The probability of damage is estimated with factors that affect the



60

three-dimensional damage extent of the ship with the given watertight subdivision (transverse,

horizontal and longitudinal). The damage parameters, such as longitudinal, vertical and

transverse extent are determined based on the geometric layout of the subject ships. Single/

multiple compartment damage are considered as per the rule requirement. Unlike the

deterministic damage stability computation which is primarily based on ship’s length, there is

no restriction on single, two compartment damage in probabilistic damage stability

calculations. Similarly, there is no restriction on machinery compartment being part of one or

two compartment damage. Also, permeability values of each compartment, tank and cargo

space are explicitly given as input for the damage stability [3]. The key points or air vent for

all the tanks are mentioned as per requirement, minimum 760 mm height from the main deck.

This key point is taken as input to calculate the immersion angle [13]. The required

subdivision index depends on ship’s length as shown in Eq. 8 [3].

R = ( )1

3

S0.002 0.0009L+ For

SL > 100.0 m (8a)

R =

( )

1

1 x100 1

S O

O

L R

R

+ −

For 80.0 m ≤ SL ≤ 100.0 m (8b)

OR in Eq. 8b is calculated as shown in Eq. 8a. The method of calculating attained

subdivision index for a ship is expressed as shown in Eq. 9.

A = 0.4 0.4 0.2A A AP LS

+ + (9)

Where the subscripts S , P and L represent the three loading conditions and ‘0.4’ and ‘0.2’

are the weighting factors. In our case ‘ S ’ corresponds to the deepest subdivision draft, ‘ P ’

corresponds to the ballast departure draft and ‘ L ’ corresponds to the ballast arrival draft. It is

understood that light draft ‘ L ’ should correspond to sailing condition only. The general

formula for computing the attained index is shown in Eq. 10.

AC

= ( )1

i t

i

p v si i i

=

=

(10)

The subscript ‘ C ’ represents one of the three loading conditions shown in Eq. 9. The

subscripts ‘ i ’ represent each investigated damage or group of damages and ‘ t ’ is the number

of damages to be investigated to calculate CA for the particular loading condition. The

probability factor ‘ip ’ is dependent on the geometry of the watertight arrangement of the

ship. In case of double hull ships, a reduction factor ‘ r ’ is computed based on the double hull

geometry. The probability that only double hull space is flooded is shown in Eq. 11a. The

probability that both the double hull space and adjacent inboard compartment is flooded is

shown in Eq. 11b.

pi = *p ri (11a)

ip = ( )* 1ip r− (11b)

The factor ‘iv ’ is dependent on the geometry of the watertight arrangement (decks) of the ship

and the draught of the initial loading condition. It represents the probability that the spaces

above the horizontal subdivision will not be flooded. The factor ‘is ’ is the survivability of



61

the ship after the considered damage for a specific initial condition. It is computed as shown

in Eq. 12.

si = ( )0.5C GZMax R

(12)

Where C =

E

E

1 if 25

0 if > 30

30 otherwise

5

E

−

(13)

MaxGZ = Maximum positive righting lever (meters) within the range as given below

but less than 0.1 m.

R = Range of positive righting lever beyond the angle of equilibrium (degrees) but not

more than 20°. The range shall be terminated at the downflooding angle.

E = final equilibrium angle of heel (degrees).

is = 0; if anyone of the downflooding points gets submerged in equilibrium condition

after damage.

The attained subdivision index is determined by adding the results from the three different

loading conditions after assigning weight to each one of them. The weighting accounts for

the corresponding percentage (40 % of summer draft, 40 % of partial loaded draft, and 20%

of lightship draft) of different loading operation [5]. The loading conditions are defined by

their mean draught and trim. The attained subdivision index shall be higher than the required

subdivision index. It is difficult to get a mathematical expression for the limiting KG and

CGL value from Eqs. 6 and 7 directly. An iterative procedure is followed to get the limiting

LSKG and LSLCG from Eqs. 6 and 7. The limiting LSKG obtained from intact stability

rules is taken as input. The probabilistic damage stability calculations are then carried out. If

the attained index is higher than the required index, the limiting LSKG is retained. Else the

LSKG is decremented by 0.1 LSKG

D% in steps and the calculations are repeated. The LSKG

which will satisfy all the damage stability rule requirements will be taken as the new limit.

The LSLCG lower/ upper limit obtained from intact stability rules is taken as input. The

probabilistic damage stability calculations are then carried out for the two values of the CGL .



62

If the attained index is higher than the required index, the limiting LSLCG values are

retained. Else the LSLCG is decremented by 0.1 LSLCG

L% in steps and the calculations are

repeated. The upper/ lower values of LSLCG which will satisfy all the rule requirements will

be taken as the new limit. Each ship design is checked for survivability in case of damage.

After summarizing all possible damage cases from the three load cases, the survivability are

estimated for single/ multiple compartment flooding. For all the methods, safety of ships

against sinking/ capsizing in case of loss of their watertight integrity is the main concern of

regulatory bodies. The analysis is concluded by computing limits of LSLCG and LSKG for

different loading condition. Finally, to evaluate survivability criteria, the attained subdivision

index must be more than the required subdivision index.

4. Results and discussion

The upper and lower limit of LSLCG for different ship types determined from intact

stability regulations is shown in Fig. 11. The LSLCG position varies according to types of

ships, hull shape (BC ,

PC ) and location of midship section. Also, LSLCG limits (upper and

lower limits) depend on the length of ship, type of cargo which the ship can carry and the

loading plan. It is noticed from the results, that the limiting range of LSLCG becomes higher

when the ship’s length increases. The length of tanker vessel varies between 120 m to 160 m

and 180 m to 250 m respectively, and the LSLCG limits varies between -0.032bp

L to -

0.037bp

L and -0.045bp

L to -0.049bp

L . Oil tanker’s LSLCG is located aft of amidships. The

trend of chemical tanker and bulk carrier is also same. Figure 11 shows that LSLCG limits

widen, when the ship’s length increases. Similarly, VLCC tanker’s have widest LSLCG

limits from -0.065bp

L to -0.078bp

L aft of midship. Also, PCC ships have smallest LSLCG

limits, when compared with other ship types. As we discussed early, LSLCG position also

varies depending on the vessel draft. In short, ship’s draft is directly proportional to cargo

density. When the VLCC tanker loaded to designed draft, the LSLCG 0.023bp

L aft of

midship. If the same ship is loaded with lighter cargo, the draft get reduces. So, the LSLCG is

shifted approximately 0.055bp

L forward. When ship’s draft reduces under water section area

also varies, it has an effect on the position of LSLCG . The detailed analysis results shown in

Fig. 11, crude oil tanker (dense cargo) have wider LSLCG limits compared with chemical

tanker (lighter cargo). The container ship’s LSLCG lies between midship to forward of

midship. The trend of PCC and LPG carrier is also similar. Container and PCC ships have

significant quantity of cargo loaded above the main deck of the vessel. As a result, LSLCG

also move towards forward compared with other ship types. Also, it is evident from Fig. 11

that container ships have LSLCG limits forward of midship as compared with PCC ship. In

case of PCC, due to extra steel ramps and decks on the forward side, the LSLCG shifts



63

forward. Similarly for LNG/ LPG carriers due to independent cargo tanks and their

insulations, membrane tanks and their insulations LSLCG shifts forward. In brief, the

LSLCG of volumetric carriers are located forward of midship, and for dead weight carriers

they are located aft of midship.

50 100 150 200 250 300 350

Lbp (m)

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Inta

ct

LC

GL

S /

Lb

p

LCG (-) aft of midshipBulk Lower Limlt

Chemical Lower Limlt

Crude Lower Limlt

LNG Lower Limlt

LPG Lower Limlt

Container Lower Limit

Pure car carrier Lower Limit

LCG (+) forward of midshipBulk Upper Limit

Chemical Upper Limit

Crude Upper Limit

LNG Upper Limit

LPG Upper Limit

Container Upper Limit

Pure car carrier upper Limit

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Midship

Fig. 11 Variation of intact LSLCG with length for different ship types.

70 140 210 280 350

Lbp (m)

0

0.5

1

1.5

2

2.5

Lim

itin

g K

G L

S /

De

pth

Bulk carrier

Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Pure car carrier

Fig. 12 Variation of limiting LSKG (intact) with length for different ship types.

The limiting LSKG for different ship types determined from intact stability regulations

is shown in Fig. 12. The LSKG non-dimensionalized by ship’s depth is plotted in the graph.

From the analysis, it is concluded that, the limiting LSKG depends on cargo density and

general arrangement. These two factors have significant contribution in limiting LSKG .

Ships which are used to carry dense cargo have higher limiting LSKG . Dead weight carrier

when loaded with high density cargo have low KG . As a result, bulk carriers have high

limiting LSKG value followed by oil tanker. The next important factor, which will affect the



64

limiting LSKG value is general arrangement. As we discussed earlier, container, PCC ships

have large quantity of cargo loaded above the main deck. As a result KG in loaded condition

is high. Therefore, as shown in Fig. 12, these ships show lower limiting LSKG value. It is

observed that the ship’s beam and depth also influence the limiting LSKG . As discussed

before, a small increase in beam leads to a significant increase of BM and thereby the

limiting LSKG of the ship. Therefore, tankers and bulk carriers having lower /L B ratio

have high limiting LSKG value. Alternately, container ships and car carriers having higher

/L B ratio have lower limiting LSKG value. Ships having lower /L B ratio will have higher

BC and vice versa.

70 140 210 280 350

Lbp (m)

0

5

10

15

20

25

Are

a u

nd

er

da

ma

ge

d

GZ c

urv

e (

m.d

eg

)Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Required area under GZ

Crude tanker validation

LNG carrier Validation

LPG carrier Validation

Fig. 13 Variation of area under DamagedGZ curve for different ship types.

70 140 210 280 350

Lbp (m)

0.5

0.6

0.7

0.8

0.9

1

Su

bd

ivis

ion

in

de

x

Bulk carrier - Attained

Container ship - Attained

Pure car carrier - Attained

Required subdivision index

Bulk carrier validation

Container ship validation

Pure car carrier validation

Fig. 14 Variation of subdivision index with length for different ship types.



65

Now we will check the influence of damage stability criteria on the LSKG and

LSLCG . The deterministic damage stability criteria requirement applicable for different ship

types are shown in Table 4. The area under the DamageGZ curve for different damage cases

is shown in Fig. 13. The results demonstrate the superior damage survivability

characteristics of the vessel as compared to the minimum rule requirement. This shows that

the internal subdivisions applied for the vessels are satisfactory. The probabilistic damage

stability criteria requirement applicable for different ship types are shown in Table 4. The

required subdivision index for each vessel was computed as per rule requirement. The

attained subdivision index was computed for 3 different loading conditions for each ship type.

These were then added after multiplying with the respective weighting factors as specified in

the rules. The variation of subdivision index for different ship types is shown in Fig. 14.

Figure 14 demonstrates that all the ship types have achieved probabilistic damage stability

requirements. For the same length, the attained subdivision index for different ship types is

different. There is contribution of geometric layout of the transverse and longitudinal

subdivision bulkheads and the DamageGZ curve.

50 100 150 200 250 300 350

Lbp (m)

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Da

ma

ge

L

CG

LS /

Lb

p

LCG (-) aft of midshipBulk Lower Limlt

Chemical Lower Limlt

Crude Lower Limlt

LNG Lower Limlt

LPG Lower Limlt

Container Lower Limit

Pure car carrier Lower Limit

LCG (+) forward of midshipBulk Upper Limit

Chemical Upper Limit

Crude Upper Limit

LNG Upper Limit

LPG Upper Limit

Container Upper Limit

Pure car carrier upper Limit

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Midship

Fig. 15 Variation of LSLCG with length for different ship types in damaged condition.

70 140 210 280 350

Lbp (m)

0

0.45

0.9

1.35

1.8

Dam

ag

ed

Lim

itin

g

KG

LS / D

ep

th

Chemical tanker

Crude tanker

LNG carrier

LPG carrier

Container carrier

Bulk carrier

Car carrier

Fig. 16 Variation of limiting LSKG with length for different ship types in damaged condition.



66

The LSLCG limits shown in Fig. 11, were checked for complying with damage stability

requirements as described earlier. The new limits are shown in Fig. 15. It is observed that

the LSLCG limits determined from intact stability criteria also comply with the damage

stability requirements. A definite trend for the limiting LSLCG cannot be observed from this

figure. However, it can be observed that LSLCG shall be less than 0.1bp

L and greater than -

0.2bp

L . The LSKG limits shown in Fig. 12 were checked for compliance with damaged

stability requirements as described earlier. The trends of damaged limiting LSKG is shown

in Fig. 16. It is observed that the damaged limiting LSKG values have decreased as

compared to intact limiting LSKG values. The damaged limiting LSKG values have

decreased up to 80 % as compared with the intact limiting LSKG values. After observing the

trends of damaged limiting LSKG in Fig. 16, it is seen that ships having higher freeboard

have a higher damaged limiting LSKG . As the ship’s size increases, the limiting LSKG

becomes higher. In case of damaged limiting LSKG , when holds are flooded with water, the

cargo remains in ship increasing the displacement of container and bulk carrier vessels. The

increased displacement leads to higher limiting LSKG value as shown in Fig. 16. On the

other hand, when damage occurs in crude oil tanker, LNG and LPG tanker, the cargo escapes

into sea or atmosphere decreasing the displacement of vessels. The decrease of displacement

reduces the limiting LSKG value as shown in Fig. 16. From Fig. 16 it is observed that for

some ship types limiting LSKG / D is > 1.0. For merchant ships this is an unlikely scenario.

This is because most of the hull weight is located at a height less than D . Only the

accommodation weight is located at a height above D . But accommodation weight is much

less as compared to other lightship weight components. In merchant ships the lightship

weight is usually much less than the deadweight component. Most of the deadweight

components are located at height less than D except in case of some volumetric carriers.

Therefore, we have the benefit of keeping the LSKG higher, although it will never be utilized

during actual ship design.

The present work is validated for each one of the ship designs, namely tanker, bulk

carrier LNG/ LPG carrier, container and car carrier. One unique vessel (9th design) is selected

for validation for oil tanker and bulk carrier. While for the other ship types the validation

vessel is chosen from the existing ship designs. The selected vessels are designed as per the

general arrangement and criteria requirement as we discussed earlier. For validation, LSLCG

is assumed as 0.3bp

L (forward of midship) for all the investigated ship types. This LSLCG is

outside the limit shown in Fig. 15. With this value of LSLCG stability criteria requirements

are checked. During this time the KG is kept as actual value. The results are presented in

Fig. 13. Figure 13 shows that crude oil tanker, and LNG/ LPG carriers do not meet the

stability requirements when LSLCG = 0.3bp

L . Similarly, it can be noticed from Fig. 14 that

bulk carrier, container and PCC ships also do not meet the stability requirements. When

LSLCG is kept outside the limit shown in Fig. 15, vessels experience unusual trim. The

excessive trim causes the vessel to fail to meet the stability requirements shown in Fig. 13.

Similarly, validation is carried out by assuming LSKG above the limit shown in Fig. 16

( LSKG = 0.3 D to 0.4 D ). During this time, the LSLCG is kept as actual value. The higher

LSKG again causes the vessels to fail to meet the damage stability requirement as shown in

the Fig. 13. The lightship weight is much less as compared to the deadweight for nearly all



67

the merchant ships. However, it can be observed that if LSLCG and LSKG exceed beyond

certain limits then the vessels will fail to meet the stability requirements. Therefore it is

important to keep this in consideration when designing new ship type.

5. Conclusions

A systematic investigation of the lightship weight distribution, limiting LSLCG and

limiting LSKG of different types of ships was carried out. Fifty eight ships of different types

and capacity was used in the analysis. The vessels were evaluated by applicable intact and

damage stability rules. On the basis of the analysis various ship designs are categorized in the

form of limiting LSLCG and LSKG .

Designers can identify the limits of design characteristics like hull, outfit, machinery

weights, HFO, diesel, fresh water, ballast water capacities, main engine power and accidental

oil outflow for a given vessel. Hence these results can be applied for the internal spaces

arrangement and distribution of weight. The results of the analysis are presented in the

number of graphs, which can give valuable guidance to the designer when verifying the

LSLCG and LSKG limits of the vessel at the early stages of design.

In LSLCG analysis, the intact and damage stability rules give the same range of

limiting forward and aft limits of LSLCG . The LSLCG for gas carriers, container ships and

PCCs are relatively more towards the forward side as compared to bulk carriers and oil

tankers. In LSKG analysis, the damage stability rules give a lower limiting values of LSKG

as compared to intact stability rules.

For merchant ships, lightship weight is less than the deadweight. Amongst merchant

ships, for deadweight carrier lightship weight is much less than the deadweight as compared

to volumetric carriers. Therefore for deadweight carriers LSKG limit may come higher than

the ship's depth. This scenario is unlikely because LSKG should be within ship's body

dimensions. Besides the lightship weight, and limiting LSKG and LSLCG , its distribution

along the ship's length is also important. This will have a significant influence on the

variation of shear force and bending moment in waves. This will be investigated in our future

work.



68

6. Reference

[1] Papanikolaou A. Ship Design Methodologies of Preliminary Design. Springer Publisher (2014).

https://doi.org/10.1007/978-94-017-8751-2

[2] Schneekluth Η. Ship design. Koehler, Herford (1985).

[3] SOLAS. Amendments to the International Convention for the Safety of Life at Sea, 1974, As Amended,

Resolution MSC. 216 (82), (2006).

[4] Simopoulos G., Konovessis D., Vassalos D. Sensitivity analysis of the probabilistic damage stability

regulations for RoPax vessels. Journal of Marine Science and Technology, Springer Japan, Vol. 13, pp.

164 - 177, (2008). https://doi.org/10.1007/s00773-007-0261-x

[5] Vassalos D. Damage stability and survivability - “nailing” passenger ship safety problems. Ships and

Offshore Structures, Vol. 9, pp. 237 - 256, (2014). https://doi.org/10.1080/17445302.2013.780397

[6] Solem S., Fagerholt K., Erikstad S. O., Patricksson Ø. Optimization of diesel electric machinery system

configuration in conceptual ship design. Journal of Marine Science and Technology, Springer Japan,

Vol. 20, pp. 406 – 416, (2015). https://doi.org/10.1007/s00773-015-0307-4

[7] Lin C. K., Shaw H. J. Preliminary parametric estimation of steel weight for new ships. Journal of Marine

Science and Technology, Springer Japan, Vol. 21, pp. 227 –239, (2016). https://doi.org/10.1007/s00773-

015-0345-y

[8] Čudina P., Bezić A. Reefer Vessel Versus Container Ship, Brodogradnja, Vol. 70, No. 1, pp. 129 - 141,

(2019). https://doi.org/10.21278/brod70109

[9] Kalajdžić M., Momčilović N. A Step Toward the Preliminary Design of Seagoing Multi-Purpose Cargo

Vessels, Brodogradnja, Vol. 71, No. 2, pp. 75 - 89, (2020). https://doi.org/10.21278/brod71205

[10] Taylor D. W. Speed and power of ships. Wiley, New York (1943).

[11] Papanikolaou A. Anastassopoulos K. Ship design and outfitting I. National Technical University of

Athens, Greece (2002).

[12] American Bureau of Shipping Rules for Building and Classing Steel Vessels, Part 3, Chapter 2, Section

1, pp. 24 - 27 (2002).

[13] ICLL, IMO Protocol relating to the International Convention on Load Lines (1966).

[14] MARPOL consolidated Edition (2006) International Convention for the Prevention of Pollution from

Ships, 1973. MARPOL consolidated Edition 2006.

[15] Ventura M. Estimation Methods for Basic Ship Design. In: University Lecture Notes in Instituto

Superior Técnico (2007).

[16] Völker H. Entwerfen von Schiffen Handbuch der Werften. In: vol XII. HANSA. Hamburg (1974).

[17] Molland A. F. The Maritime Engineering Reference Book: A Guide to Ship Design, Construction and

Operation. Butterworth-Heinemann, Portugal (2008).

[18] Papanikolaou A. Ship design methodologies of preliminary ship design. Symeon Publisher, Athens,

Greece (2009).

[19] MARPOL New Regulation 12 A – Oil fuel tank protection, (2006).

[20] Explanatory notes on matters related to the accidental oil outflow performance under regulation 23 of the

revised MARPOL Annex I. Resolution MEPC. 122 (52), (2004).

[21] Amendments to the International Code for the Construction and Equipment of Ships Carrying Liquefied

Gases in Bulk, Resolution MSC. 370 (93) (2014).

Nomenclature

A Attained subdivision index

B Breadth of ship

BM Distance between center of buoyancy to metacenter

https://doi.org/10.1007/978-94-017-8751-2

https://doi.org/10.1007/s00773-007-0261-x

https://doi.org/10.1080/17445302.2013.780397

https://doi.org/10.1007/s00773-015-0307-4

https://doi.org/10.1007/s00773-015-0345-y

https://doi.org/10.1007/s00773-015-0345-y

https://doi.org/10.21278/brod70109

https://doi.org/10.21278/brod71205



69

/B T Ratio of breath to draft

BC Block coefficient

PC Prismatic coefficient

MC Midship section coefficient

D Depth of ship

Dd Deepest subdivision draught

Pd Partial subdivision draught

Ld Light service draught

Fr Froude number

FEU Forty equivalent units

GM Distance between center of gravity to metacenter

GZ Righting lever

MaxGZ Maximum positive righting lever

TGM Transverse metacentric height

HFO Heavy fuel oil

IGC International Gas Carrier Code

IMO International Maritime Organization

KG Distance between Keel to center of gravity

LSKG Lightship Keel to center of gravity distance

bpL Length between perpendiculars

SL Length of ship

LNG Liquefied natural gas

LPG Liquefied petroleum gas

/L D Ratio of length to depth

/L B Ratio of length to breath

CGL Longitudinal center of gravity

LSLCG Lightship longitudinal center of gravity

CBL Longitudinal center of buoyancy

MARPOL International Convention for the Prevention of Pollution from Ships

TCM Moment to change trim by 1 cm

OPA Oil pollution act

BO Bottom oil outflow

MO Mean oil outflow

SO Side oil outflow

P Propulsive power



70

pi Probability factor

r Reduction factor

R Required subdivision index

si Survivability factor

T Draft of ship

TEU Twenty equivalent units

V Speed of ship

LSW Weight of lightship

MEW Weight of all the machinery located in the engine room

OTW Weight of the equipment, outfit, deck machinery, etc.

STW Weight of the hull structure, the superstructure and the outfit steel

(machinery foundations, supports, masts, ladders, handrails, etc.).

R Range of positive righting lever beyond the angle of equilibrium

E Final equilibrium angle of heel

Displacement of ship

Submitted: 15.10.2019.

Accepted: 20.08.2020.

Author 1, Sree Krishna Prabu Chelladurai

Research scholar

Department of Ocean Engineering & Naval Architecture

Indian Institute of Technology Kharagpur

Kharagpur-721302, West Bengal, India

Author 2, Dr. Vishwanath Nagarajan,

Associate Professor,




email: [email protected]

Author 3, Om Prakash Sha

Professor,




mailto:[email protected]

study on the lightship characteristics of …

Documents